Endogenous Second Moments: A Unified Approach to Fluctuations in Risk, Dispersion, and Uncertainty

40 Pages Posted: 20 Jun 2016 Last revised: 10 Mar 2018

See all articles by Ludwig Straub

Ludwig Straub

Massachusetts Institute of Technology (MIT), Department of Economics, Students

Robert Ulbricht

Boston College

Date Written: March 7, 2018

Abstract

Many important statistics in macroeconomics and finance — such as cross-sectional dispersions, risk, volatility, or uncertainty — are second moments. In this paper, we explore a mechanism by which second moments naturally and endogenously fluctuate over time as nonlinear transformations of fundamentals. Specifically, we provide general results that characterize second moments of transformed random variables when the underlying fundamentals are subject to distributional shifts that affect their means, but not their variances. We illustrate the usefulness of our results with a series of applications to (1) the cyclicality of the cross-sectional dispersions of macroeconomic variables, (2) the dispersion of MRPKs, (3) security pricing, and (4) endogenous uncertainty in Bayesian inference problems.

Keywords: Cross-Sectional Dispersion, Endogenous Uncertainty, Nonlinear Transformations, Risk, Second Moments, Volatility

JEL Classification: C19, D83, E32, G13

Suggested Citation

Straub, Ludwig and Ulbricht, Robert, Endogenous Second Moments: A Unified Approach to Fluctuations in Risk, Dispersion, and Uncertainty (March 7, 2018). Available at SSRN: https://ssrn.com/abstract=2796141 or http://dx.doi.org/10.2139/ssrn.2796141

Ludwig Straub

Massachusetts Institute of Technology (MIT), Department of Economics, Students ( email )

Cambridge, MA
United States

Robert Ulbricht (Contact Author)

Boston College ( email )

United States

HOME PAGE: http://www.robertulbricht.com/

Register to save articles to
your library

Register

Paper statistics

Downloads
67
Abstract Views
365
rank
339,870
PlumX Metrics